Fraction calculator
This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.
The result:
1.5 - 1 1/5 = 3/10 = 0.3
Spelled result in words is three tenths.How do we solve fractions step by step?
- Conversion a decimal number to a fraction: 1.5 = 15/10 = 3/2
a) Write down the decimal 1.5 divided by 1: 1.5 = 1.5/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
1.5/1 = 15/10
Note: 15/10 is called a decimal fraction.
c) Simplify and reduce the fraction
15/10 = 3 * 5/2 * 5 = 3* 5/2* 5= 3/2 - Conversion a mixed number 1 1/5 to a improper fraction: 1 1/5 = 1 1/5 = 1 · 5 + 1/5 = 5 + 1/5 = 6/5
To find a new numerator:
a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5
b) Add the answer from the previous step 5 to the numerator 1. New numerator is 5 + 1 = 6
c) Write a previous answer (new numerator 6) over the denominator 5.
One and one fifth is six fifths. - Subtract: 1.5 - 6/5 = 3/2 - 6/5 = 3 · 5/2 · 5 - 6 · 2/5 · 2 = 15/10 - 12/10 = 15 - 12/10 = 3/10
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 5) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 5 = 10. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - three halfs minus six fifths is three tenths.
Rules for expressions with fractions:
Fractions - use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.Mixed numerals (mixed numbers or fractions) keep one space between the integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.
Math Symbols
Symbol | Symbol name | Symbol Meaning | Example |
---|---|---|---|
+ | plus sign | addition | 1/2 + 1/3 |
- | minus sign | subtraction | 1 1/2 - 2/3 |
* | asterisk | multiplication | 2/3 * 3/4 |
× | times sign | multiplication | 2/3 × 5/6 |
: | division sign | division | 1/2 : 3 |
/ | division slash | division | 1/3 / 5 |
: | colon | complex fraction | 1/2 : 1/3 |
^ | caret | exponentiation / power | 1/4^3 |
() | parentheses | calculate expression inside first | -3/5 - (-1/4) |
Examples:
• adding fractions: 2/4 + 3/4• subtracting fractions: 2/3 - 1/2
• multiplying fractions: 7/8 * 3/9
• dividing Fractions: 1/2 : 3/4
• reciprocal of a fraction: 1 : 3/4
• square of a fraction: 2/3^2
• cube of a fraction: 2/3^3
• exponentiation of a fraction: 1/2^4
• fractional exponents: 16 ^ 1/2
• adding fractions and mixed numbers: 8/5 + 6 2/7
• dividing integer and fraction: 5 ÷ 1/2
• complex fractions: 5/8 : 2 2/3
• decimal to fraction: 0.625
• Fraction to Decimal: 1/4
• Fraction to Percent: 1/8 %
• comparing fractions: 1/4 2/3
• multiplying a fraction by a whole number: 6 * 3/4
• square root of a fraction: sqrt(1/16)
• reducing or simplifying the fraction (simplification) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction
• expression with brackets: 1/3 * (1/2 - 3 3/8)
• compound fraction: 3/4 of 5/7
• fractions multiple: 2/3 of 3/5
• divide to find the quotient: 3/5 ÷ 2/3
The calculator follows well-known rules for the order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must evaluate from left to right.
Fractions in word problems:
- Peter's calculation
Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2 . Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect.
- A man 9
A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents?
- A less than B
What is 3/5 less than 11/12? (Answer should be in proper or improper only: Example 1/2, -1/2, 3/2, and -3/2)
- Mr. Vandar
Mr. Vandar washed 1/4 of his laundry. His son washed 2/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
- Cherries 2
If a farmer reaped 636 cherries and he sold one-third to a shopkeeper, how many did he retain?
- A cake
A cake has 46 slices. Harry ate 16 slices, and Jack ate 26 slices, Dave ate 0 & Mary ate 1 slice. What fraction of the cake is remaining?
- Shopper
Eva spent 1/4 in one store and 1/3 in another. What fraction is left?
- Sundar
Sundar has 50 chocolates. He gave 2/5 of these chocolates to Ram and ate 1/5 of them. How many chocolates are left with Sundar?
- The bread 2
Sandra and Tylar baked two loaves of bread. On Monday, they ate 1/2 of one loaf. On Tuesday, they ate 1/3 of one loaf of bread. How much bread is left?
- Terrell
Terrell goes apple-picking. He uses 3/10 of his apples. Then he uses 5/10. What fraction of his apples does he have left?
- Difference of two fractions
What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. )
- Fraction expression
Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
- Evaluate - lowest terms
Evaluate: 16/25 - 11/25 (Express answer as a fraction reduced to lowest terms. )
- From a
From a 1-meter ribbon, Ericka cut 2/4 meters for her hat and another 1/4 meters for her bag. How long was the remaining piece?
- Difference between fractions
What is the difference when you take away 1/6 from 2/8?
more math problems »